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It has 104 edges and 52 vertices and is currently the smallest known example of a 4-regular matchstick graph. [3] It is a rigid graph. [4] Every 4-regular matchstick graph contains at least 20 vertices. [5] Examples of 4-regular matchstick graphs are currently known for all number of vertices ≥ 52 except for 53, 55, 56, 58, 59, 61 and 62.
Every matchstick graph is a planar graph, [14] but some otherwise-planar unit distance graphs (such as the Moser spindle) have a crossing in every representation as a unit distance graph. Additionally, in the context of unit distance graphs, the term 'planar' should be used with care, as some authors use it to refer to the plane in which the ...
207 is a Wedderburn-Etherington number. [1] There are exactly 207 different matchstick graphs with eight edges. [2] [3] 207 is a deficient number, as 207's proper divisors (divisors not including the number itself) only add up to 105: + + + + = <.
As a planar Laman graph, it is the graph of a pointed pseudotriangulation, meaning that it can be embedded in the plane in such a way that the unbounded face is the convex hull of the embedding and every bounded face is a pseudotriangle with only three convex vertices. [9] The complement graph of the Moser graph is a triangle-free graph. Thus ...
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The price of gold has surpassed numerous records over the last year. / Credit: Getty Images/iStockphoto
In graph theory, a star S k is the complete bipartite graph K 1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1).Alternatively, some authors define S k to be the tree of order k with maximum diameter 2; in which case a star of k > 2 has k − 1 leaves.